Finite Group Databasebeta

← #34100235

Subgroups — #34100235

Order 20096.

306 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757237C211yesmaximal, characteristic
2C4×C22⋊Dic157C211yesmaximal, characteristic
3#23757032C214yesmaximal, complemented
4C2×#117×C157C211yesmaximal, characteristic
5C2×#14578938C2212yes—
6C2×C22⋊Dic157—21no—
7C2×C4×Dic157C2212yes—
8C22⋊#11929434—21no—
9C22⋊#11929434—21no—
10#19097678—21no—
11C23×C4×C157C2211yescharacteristic
12#117×C157—21no—
13#117×C157—21no—
14#117×C157C412yescomplemented
15#117×C157C2212yes—
16C2×C4⋊C4×C157C411yescharacteristic, complemented
17C2×C4⋊C4×C157C411yescharacteristic, complemented
18C2×C22⋊C4×C157—21no—
19C2×C42×C157—21no—
20C22×Dic157—22no—
21#14578938—24no—
22C2×#11929434—22no—
23C22⋊Dic157—24no—
24C4×Dic157—24no—
25C24×C157D411yescharacteristic
26C22×C4×C157—24no—
27C22×C4×C157—21no—
28C22×C4×C157—21no—
29C22×C4×C157C2×C411yescharacteristic
30C22×C4×C157C2×C411yescharacteristic
31C22×C4×C157D411yescharacteristic
32C22×C4×C157D411yescharacteristic
33C22×C4×C157D411yescharacteristic
34C22×C4×C157C2311yescharacteristic
35C4⋊C4×C157—21no—
36C4⋊C4×C157—21no—
37C4⋊C4×C157C2×C412yes—
38C4⋊C4×C157C2×C412yes—
39C22⋊C4×C157—22no—
40C22⋊C4×C157—22no—
41C42×C157—22no—
42C42×C157—22no—
43C2×Dic157—24no—
44C2×Dic157—42no—
45C2×Dic157—42no—
46#11929434—42no—
47C23×C157—22no—
48C23×C157—22no—
49C23×C157—41no—
50C23×C157C22⋊C411yescharacteristic
51C23×C157C22⋊C411yescharacteristic
52C23×C157C2×D411yescharacteristic
53C2×C4×C157—22no—
54C2×C4×C157—22no—
55C2×C4×C157—22no—
56C2×C4×C157—22no—
57C2×C4×C157—22no—
58C2×C4×C157—22no—
59C2×C4×C157—22no—
60C2×C4×C157—42no—
61C2×C4×C157—42no—
62C2×C4×C157C22⋊C411yescharacteristic
63C2×C4×C157C22⋊C411yescharacteristic
64C2×C4×C157C22×C411yescharacteristic
65C2×C4×C157C2×D411yescharacteristic
66C2×C4×C157#4114yes—
67C22×C157—21no—
68C22×C157—21no—
69C22×C157—21no—
70C22×C157—21no—
71C22×C157—21no—
72C22×C157—21no—
73C22×C157—21no—
74C22×C157—44no—
75C22×C157#10412yes—
76C22×C157C2×C22⋊C411yescharacteristic
77C22×C157#12312yes—
78C4×C157—21no—
79C4×C157—21no—
80C4×C157—42no—
81C4×C157—42no—
82C4×C157#11712yes—
83C4×C157#12312yes—
84Dic157—44no—
85C2×C157—22no—
86C2×C157—22no—
87C2×C157—41no—
88C2×C157#38111yescharacteristic
89C2×C157C2×#10411yescharacteristic
90C2×C157#42111yescharacteristic
91C157#182611yescharacteristic, complemented, Sylow
92#1826—1571nomaximal, Sylow
93C2×#117D15711yescharacteristic
94#407—1571no—
95C4×C22⋊C4—1571no—
96#339—1574no—
97C23×C4C2×D15711yescharacteristic
98C2×M16—1572no—
99#117—21no—
100#117—21no—
101#117Dic15712yescomplemented
102#117C2×D15712yes—
103C2×C4⋊C4Dic15711yescharacteristic, complemented
104C2×C4⋊C4Dic15711yescharacteristic, complemented
105C2×C22⋊C4—21no—
106C2×C22⋊C4—3141no—
107C2×C42—21no—
108C2×C42—1572no—
109C22⋊C8—3141no—
110C22⋊C8—3141no—
111#95—3141no—
112C24C22⋊D15711yescharacteristic
113C22×C4—24no—
114C22×C4—21no—
115C22×C4—21no—
116C22×C4—3142no—
117C22×C4C2×Dic15711yescharacteristic
118C22×C4C2×Dic15711yescharacteristic
119C22×C4C22⋊D15711yescharacteristic
120C22×C4C22⋊D15711yescharacteristic
121C22×C4C22⋊D15711yescharacteristic
122C22×C4C22×D15711yescharacteristic
123M16—3144no—
124C2×C8—3142no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4C2×Dic15712yes—
128C4⋊C4C2×Dic15712yes—
129C22⋊C4—22no—
130C22⋊C4—22no—
131C22⋊C4—3144no—
132C42—22no—
133C42—22no—
134C42—3144no—
135C23—22no—
136C23—22no—
137C23—41no—
138C23C22⋊Dic15711yescharacteristic
139C23C22⋊Dic15711yescharacteristic
140C23C2×C22⋊D15711yescharacteristic
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—42no—
149C2×C4—42no—
150C2×C4—3144no—
151C2×C4—6282no—
152C2×C4—6282no—
153C2×C4C22⋊Dic15711yescharacteristic
154C2×C4C22⋊Dic15711yescharacteristic
155C2×C4C22×Dic15711yescharacteristic
156C2×C4C2×C22⋊D15711yescharacteristic
157C2×C4#1457895414yes—
158C8—6282no—
159C22—21no—
160C22—21no—
161C22—21no—
162C22—21no—
163C22—21no—
164C22—21no—
165C22—21no—
166C22—44no—
167C22#1909769812yes—
168C22C2×C22⋊Dic15711yescharacteristic
169C22#1909775412yes—
170C4—21no—
171C4—21no—
172C4—42no—
173C4—42no—
174C4—6284no—
175C4#1909773012yes—
176C4#1909775412yes—
177C2—22no—
178C2—22no—
179C2—41no—
180C2#2375713611yescharacteristic
181C2C2×#1909769811yescharacteristic
182C2#2375729011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D157
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
FittingC2×#117×C157C2
socleC22×C157C2×C22⋊C4
prime radicalC24×C157D4
cosocleC22×C4×C157C23
hypercenterC2×#117D157
hypocenterC157#1826
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #23757032C2semidirect
14. #117×C157C4semidirect
16. C2×C4⋊C4×C157C4semidirect
17. C2×C4⋊C4×C157C4semidirect
91. C157#1826semidirect
101. #117Dic157semidirect
103. C2×C4⋊C4Dic157semidirect
104. C2×C4⋊C4Dic157semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237572372
C4×C22⋊Dic1572
#237570322
C2×#117×C1572
#1826157